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Abstract

Moment invariants of the Fourier transform of an image are introduced. It is found that a feature set composed of moment invariants from both the space domain and the Fourier domain gives better performance for a wide range of classification tasks than does the same number of moment invariants from either domain alone. Redundancy among moments of the two domains is examined by using the correlation coefficient between the feature kernels as a measure. Examples are used to compare the feature sets and to assess their performance in classification tasks. Moment invariants of the magnitude of the Fourier transform and, by inference, some popular features, such as the spectral ring–wedge detector, are found to fall far short in performance compared with those in which the phase of the Fourier transform is also utilized. Coherent optical systems to compute the dual-domain moment invariants are proposed.

References

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a The 16 moment invariants used in the examples. Feature numbers 1–16 indicate moment invariants based on space-domain complex moments, and numbers 17–32 indicate those based on frequency-domain complex moments. The complex moments referred to here are the result of scale and contrast normalizations as described in Section 2.

a In each, 16 moment invariants were used; column headings indicate the domains of the moment invariants. Where applicable, numbers of the best 16 Sures parentheses m order of importance. The underlined numbers make up more than 90% of the total divergence attributed to the best 16 of 32 features.

a The 16 moment invariants used in the examples. Feature numbers 1–16 indicate moment invariants based on space-domain complex moments, and numbers 17–32 indicate those based on frequency-domain complex moments. The complex moments referred to here are the result of scale and contrast normalizations as described in Section 2.

a In each, 16 moment invariants were used; column headings indicate the domains of the moment invariants. Where applicable, numbers of the best 16 Sures parentheses m order of importance. The underlined numbers make up more than 90% of the total divergence attributed to the best 16 of 32 features.